Using the genfit() function, fit the curve to the results
of SelectChannels(41,96) and determine the 6 parameters
A0..A5 [3 marks]

Leaving the centre channel fixed, write a section of
MathCAD to produce a graph showing how the Peak Width
Characteristic (A3) varies as the number of channels
in the average is varied from 1 to 100. [3 marks]

which may be characterisied by the following parameters:

A0: Background level

A1: Amplitude of Peak #1

A2: Centre of Peak #1

A3: Peak width Characteristic

A4: Amplitude of Peak #2

A5: Centre of Peak #2

Question
8

T
he data file http://users.aber.ac.uk/dpl/ph36010/handouts/KEScan.csv
contains the results of
using the above detector in an electron spectrometer.

The first column in the data file gives the Kinetic
Energy of electrons passing through the centre of an
analyser containing the detector. The remaining 192
columns in the data give the number of electrons falling
on the 192 channels of the detector in one second at
each Kinetic Energy.

In this application, the data from a number of adjacent
channels will be averaged.

Copy the data file to your own filestore and create
a file read component to read the data into an array.

Create a function SelectChannels(width,centre) which
returns a vector containing the averaged readings over
'width' detectors centred on detector 'centre'. Thus
SelectChannels(41,96) will return a vector showing
the average number of counts recieved on channels 75
to 116 for each Kinetic Energy. [3 marks]

The equation of a curve containing two gaussian peaks
is given by the formula:

Question
7

During evaluation of an ion counting detector an experiment
was conducted to compare the performance of the new
detector with an existing photomultiplier based detector.
What is particularly interesting is the maximum count
rate delivered by the counting detector and how linear
the device is.

In the experiment a beam of ions was switched between
the ion counting detector and a photomultiplier. At
each point the photomultiplier current was recorded
along with the count rate observed on the ion counting
detector. The incident beam was varied in intensity
over several orders of magnitude.

holds the results of this experiment. The first column
holds the photomultiplier in uA and the second the
count rate recorded on the ion detector in counts per
second.

Use a file read component to read in the datafile. [1
mark]

Plot the data on a graph with log/log axes.
[1 mark]

According to theory, the response of such a detector
should follow a curve

given by y=x*A*exp(-B*x), where A is a scale factor
and A/B is the time it takes the counting detector
to recover between events. Use a curve fitting routine
and determine the constants A & B. [4 marks]

Plot the fitted curve on the same log/log plot as the
experimental data [1 mark]

By scaling the photomulitplier current by an appropriate
factor, you should be able to plot the observed count
rate of the detector against the incident count rate,
again use log/log axes. [1 mark]

Determine the time in seconds it takes the detector
to recover after an event. [2 marks]

Question
6

Copy and paste the example from PH15010 Worksheet 6
about the photoelectric effect. Your example should
start with an input table holding the stopping potential
data and finish with calculation of the threshold frequency
and Planck's constant. [10 marks]

over a range of x-values from 0 to 1, using a suitable
increment for x [2 marks]

Calculate the area under the curve, using both symbolic
and numeric methods. [3 marks]

Using the above result, together with the area of the
unit square, devise a

method for determining a value for p
which works by calculating the proportion of points
picked at random from within the unit square which
lie under the above curve. [5 marks]

Functions that you may find helpful for this problem
are:

rnd(), if() and mean()

Question
5

Plot the curve:

Question
4.

A sphere of lead of radius 6 inches is dropped from
a height of 4 feet.

Calculate the surface area, volume and mass of the sphere,
displaying your results in both metric and imperial
units. [3 marks]

Write a function, hsphere(), giving the height of the
sphere above the ground as a function of time after
the sphere is released. [2 marks]

Write a function, vsphere(), giving the velocity of
the sphere as a function of time after the sphere is
released. [2 marks]

Draw a graph showing the height of the sphere as a function
of time. [2 marks]

Detemine the time that the sphere will hit the ground.
[2 marks]

Calculate the velocity (in m/s) that the sphere will
hit the ground.(You may neglect air resistance) [2
marks]

Calculate the kinetic energy (in Joules) of the sphere
as it hits the ground. [2 marks]

Question
3.

The file http://users.aber.ac.uk/dpl/ph36010/handouts/RValues.txt
contains the values of a number of resistors. Copy
this file into your own directory.

Create a file read component to read these values into
a vector. [2 marks]

Determine the value of the largest, the smallest, the
mean and standard deviation along with the total number
of resistors. [5 marks]

Create a histogram graph of the values, using an appropriate
number of bins to cover the range of values. [5 marks]

Question
2. [4 marks]

Solve the following set of simultaneous equations, using
any appropriate technique:

Question
1. [4 marks]

Calculate the surface area, volume and mass of a right
circular cone made from quartz. The dimensions of the
cone are: base radius 7cm, height 10cm.

This worksheet is a marked assignment to test what you
have learned from the course.

This assignment will count towards 50% of the module
marks, the remaining 50% will come from the project.

The answers to the exercises should form a single worksheet.
Completed worksheets should be emailed to dpl@aber.ac.uk
by 23:59 on 17/5/03.

Please ensure that your name appears on the right hand
side of the page header and that your email identifier
appears on the left hand side of the page footer.

Marks will be given for correctness, layout style, comments,
use of units and creative use of material covered in
the course. [style=5 marks]

In order to complete the exercises, you may have to
do research in the mathCAD resource centre.